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Fe3Al2Si3O12 +KMg3AlSi3O10(OH)2 ↔ Mg3Al2Si3O12 +KFe3AlSi3O10(OH)2
Almandine + Phlogopite ↔ Pyrope + Annite
The garnet-biotite geothermometer estimates temperature at equilibrium condition using Fe and Mg partition coefficient between garnet and biotite. For temperature calculation, two experimental equilibrium constant and temperature relationships were used. First method is by ideal mixing model for garnet and biotite after Ferry and Spear (1978): lnKD = (2109/T)–0.782. The second one is by non-ideal mixing model for garnet and biotite after Perchuk and Lavrentéva (1983): lnKD = (3948/T)–2.87.
In the calculation of equilibrium temperature, I followed analytical protocol of the Spear (1991) and Spear and Florence (1992) to estimate the peak equilibrium conditions: In this protocol garnet and biotite included within feldspar and quartz without other mineral inclusions were selected for analysis to minimize the potential retrograde Fe-Mg exchange and maximize the potential for retaining peak equilibrium KD (garnet-biotite). Moreover, Sajeev and Osanai (2005) avoided applying the geothermometer to biotite and garnet in contact each other to minimize the effect of retrograde metamorphic process. I also followed their method. Petrographic observation and microprobe line-scan analyses of garnet and biotite were done to ensure the mineral contact condition and the chemical homogeneity. The garnets from the garnet-biotite gneiss, garnet-biotite-cordierite gneiss, and charnockitic gneiss with garnet were used in calculation of equilibrium temperature.
However, the garnets in hornblende-bearing charnockitic gneiss were not used due to higher grossular content.
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Application of garnet-biotite geotherm for garnet-biotite gneiss 17-24GB
Figure 12a shows the mineral assemblage of garnet and biotite in the garnet-biotite gneiss 17-24GB. Three types of occurrences of biotites are observed: biotite inclusions in garnet, which is designated as Bt1; biotite at the edge of garnet, designated as Bt2 and Bt3;
and biotite in the matrix, designated as Bt4. However, B4 biotites are not in contact with garnet. The representative equilibrium temperatures of garnet and Bt1 was given as 629 ± 11 °C by applying ideal mixing model after Ferry and Spear (1978) and as 611 ± 8 °C by non-ideal mixing model after Perchuk and Lavrentéva (1983). The representative temperatures of garnet and Bt2 are given as 584 ± 10 °C by ideal mixing model and as 587 ± 7 °C by non-ideal mixing model, whereas the representative equilibrium temperatures of garnet and Bt3 are 716 ±12 °C by the ideal mixing model and as 654 ± 8 °C by non-ideal mixing model. The representative equilibrium temperatures of garnet and Bt4 are calculated as 660 ± 11 °C by the ideal mixing model and as 627 ± 8 °C by non-ideal mixing model.
Table 14 Calculated equilibrium temperature (°C) by garnet and biotite in17-24GB
Sample kbar
Representative equilibrium temp. by ideal mixing model after Ferry and Spear (1978)
Representative equilibrium temp.
by non-ideal mixing model after Perchuk and Lavrentéva (1983)
Bt1 2-10 629±11 611±8
Bt2 2-10 584±10 587±7
Bt3 2-10 716±12 654±8
Bt4 2-10 660±11 627±8
Application of garnet-biotite geotherm for garnet-biotite cordierite gneiss 23-32Co Figure 12b shows the mineral assemblage of garnet and biotite in garnet-biotite-cordierite gneiss. Three modes of occurrences of biotites were observed: biotite inclusions in garnet, designated as Bt5; biotite at the edge of garnet, designated as B6; and biotite in the matrix, designated as B7. Biotites (B7) are not in contact with garnet. The representative equilibrium temperatures of garnet and Bt5 are given as 631 ± 11 °C by the ideal mixing model and 612 ± 8 °C by non-ideal mixing model. The representative equilibrium
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temperatures of garnet and Bt6 are calculated as 868 ± 14 °C by the ideal mixing model 722 ± 9°C by non-ideal mixing model. The representative temperatures of garnet and Bt7 are 733 ± 12 °C by the ideal mixing model and 662 ± 8 °C by non-ideal mixing model.
Table 15 Calculated equilibrium temperature (°C) by garnet and biotite in 23-32Co
Sample kbar
Representative equilibrium temp. by ideal mixing model after Ferry and Spear (1978)
Representative equilibrium temp. by non-ideal mixing model after Perchuk and
Lavrentéva (1983)
Bt5 2-10 631±11 612±8
Bt6 2-10 868±14 722±9
Bt7 2-10 733±12 662±8
Application of garnet-biotite geotherm for garnet-biotite gneiss 14-21GB
Figure 12c shows the mineral assemblage of garnet and biotite in garnet-biotite gneiss (14-21GB). Two modes of occurrences of biotites were observed: biotite inclusions in garnet, designated as Bt8; and biotite at the edge of garnet, designated as Bt9. The representative equilibrium temperatures of garnet and Bt5 are given as 640 ± 11 °C by the ideal mixing model and 617 ± 8 °C by non-ideal mixing model. The representative equilibrium temperatures of garnet and Bt6 are calculated as 825 ± 13 °C by the ideal mixing model 704 ± 8°C by non-ideal mixing model.
Table 16 Calculated equilibrium temperature (°C) by garnet and biotite in 14-21GB
Sample kbar
Representative equilibrium temp. by ideal mixing model after Ferry and Spear (1978)
Representative equilibrium temp. by non-ideal mixing model after Perchuk
and Lavrentéva (1983)
Bt8 2-10 640±11 617±8
Bt9 2-10 825±13 704±8
Application of garnet-biotite geotherm for garnet-biotite gneiss 07-10GB
Figure 12d shows the mineral assemblage of garnet and biotite in the garnet-biotite gneiss 07-10GB. Two types of occurrences of biotites are observed: biotite at the edge of garnet, designated as Bt10; and biotite in the matrix, designated as Bt11. Biotites (B11) are not in contact with garnet. The representative equilibrium temperatures of garnet and Bt10
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was given as 703 ± 12 °C by applying ideal mixing model after Ferry and Spear (1978) and as 648 ± 8 °C by non-ideal mixing model after Perchuk and Lavrentéva (1983). The representative temperatures of garnet and Bt11 are given as 764 ± 12 °C by ideal mixing model and as 677 ± 8 °C by non-ideal mixing model.
Table 17 Calculated equilibrium temperature (°C) by garnet and biotite in 07-10GB
Sample kbar
Representative equilibrium temp.
by ideal mixing model after Ferry and Spear (1978)
Representative equilibrium temp. by non-ideal mixing model after Perchuk and
Lavrentéva (1983)
Bt10 2-10 703±12 648±8
Bt11 2-10 764±12 677±8
Application of garnet-biotite geotherm for charnockitic gneiss 04-05 C
Figure 12e shows the mineral assemblage of garnet and biotite in charnockitic gneiss.
Two modes of occurrences of biotites were observed: biotite at the edge of garnet, designated as B12; and biotite in the matrix, designated as B13. Biotites (B13) are not in contact with garnet. The representative equilibrium temperatures of garnet and Bt12 are given as 710 ± 12 °C by the ideal mixing model and 651 ± 8 °C by non-ideal mixing model. The representative equilibrium temperatures of garnet and Bt13 are calculated as 868 ± 14 °C by the ideal mixing model 722 ± 9°C by non-ideal mixing model.
Table 18 Calculated equilibrium temperature (°C) by garnet and biotite in 04-05C
Sample kbar
Representative equilibrium temp. by ideal mixing model after Ferry and Spear (1978)
Representative equilibrium temp. by non-ideal mixing model after Perchuk and
Lavrentéva (1983)
Bt12 02-10 710±12 651±8
Bt13 02-10 764±13 677±8
Application of garnet-biotite geotherm for garnet-biotite gneiss 11-17GB
Figure 12f shows the mineral assemblage of garnet and biotite in garnet-biotite gneiss.
One mode of occurrences of biotites was observed: biotite at the edge of garnet, designated as B14. The representative equilibrium temperatures of garnet and Bt14 are given as 555 ± 10 °C by the ideal mixing model and 571 ± 7 °C by non-ideal mixing model.
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Table 19 Calculated equilibrium temperature (°C) by garnet and biotite in 11-17GB
Sample kbar
Representative equilibrium temp. by ideal mixing model
after Ferry and Spear (1978)
Representative equilibrium temp. by ideal mixing model after Ferry and
Spear (1978)
Bt14 2-10 555±10 571±7
Application of garnet-biotite geotherm for garnet-biotite gneiss 03-04GB
Figure 12g shows the mineral assemblage of garnet and biotite in garnet-biotite gneiss.
Two modes of occurrences of biotites were observed: biotite at the edge of garnet, designated as B15; and biotite in the matrix, designated as B16. Biotites (B16) are not in contact with garnet. The representative equilibrium temperatures of garnet and Bt15 are given as 717 ± 12 °C by the ideal mixing model and 655 ± 8 °C by non-ideal mixing model. The representative equilibrium temperatures of garnet and Bt16 are calculated as 729 ± 12 °C by the ideal mixing model 660 ± 8 °C by non-ideal mixing model.
Table 20 Calculated equilibrium temperature (°C) by garnet and biotite in 03-04GB
Sample kbar
Representative equilibrium temp. by ideal mixing model
after Ferry and Spear (1978)
Representative equilibrium temp. by ideal mixing model after Ferry and
Spear (1978)
Bt15 02-10 717±12 655±8
Bt16 02-10 729±12 660±8
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Tables 21 show a summary of the average of calculated KD values and estimated representative equilibrium temperature for the samples in this study.
Table 21 Average KD values and Estimated equilibrium temperature (T) for the Fe-Mg exchange between garnet and biotite
Sample no 17-24GB 14-21GB 07-10GB 11-17GB 03-04GB 04-05GB 23-32Co
n 24 13 64 10 14 24 28
KD 3.872 3.651 3.227 3.657 3.762 3.553 3.267
lnKD 1.354 1.295 1.172 1.297 1.325 1.268 1.184
T (°C) Sp (by ideal mixing
model) 737±13 765±14 831±15 764±14 751±14 779±14 824±15
T(°C) Per ( by non-ideal
mixing model) 683±9 696±9 726±9 696±9 689±9 703±9 723±9
Average 710±11 730±12 778±12 730±12 720±12 741±12 774±12
Sp: Ferry and Spear (1978), Per: Perchuk and Lavrentéva (1983)
As described already, the typical petrographic characteristics formed by the metamorphism are (1) formation of orthopyroxene and porphyroblastic garnet (Fig. 9a, b, c, d, and g) in prograde metamorphism (Perera, 1987, 1994); (2) breakdown of garnet (Fig. 9g) in the isothermal decompression stage before reaching the peak temperature (Perera, 1987, 1994); and (3) crystallization of secondary garnet (Fig. 9h) in the isobaric cooling stage (Perera, 1987, 1994). According to the estimated equilibrium temperatures using biotite-garnet assemblages, the calculated average temperature for porphyroblastic biotite-garnets in the sample 11-17GB is ~764 °C, whereas the secondary garnet in the same sample gave the temperature of ~550 °C. This difference of temperatures between the porphyroblastic garnets and the secondary garnets suggests that formation of porphyroblastic garnet and breakdown of garnet has taken place at temperatures of 850–750 °C and the secondary garnet formation by retrograde isobaric cooling process at ~550 °C. Such difference of estimated metamorphic temperatures was only observed in the zircons from the granulite facies metamorphic rocks in
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the study area. This may indicate the existence of several thermal events or repeated thermal events during the final metamorphic event. The thin peripheral overgrowths in zircon grains may have been formed by this final metamorphic event.
Based on the present results, contour lines of temperature can be drawn as shown in Figure 36. Sajeev and Osanai (2005) also proposed distribution of metamorphic temperatures of whole Southwest Highland Complex including the same area as this study. Sajeev and Osanai (2005) used average temperatures from four conventional thermometers as Thopmpson (1979), Ferry and Spear (1978), Perchuk and Lavrenteva (1983), and Perchuck et al. (1985). However, their conclusions were derived using the results from three samples which were not sufficient in amount to establish contour map for the SWHC. In this study, I analyzed seven samples, and, by combining Sajeev and Osanai (2005), the metamorphic temperature contour map in Figure 36 is more reliable and accurate. According to this result, eastern and southern areas tend to show higher temperatures, which is similar to that by Sajeev and Osanai (2005) but more complicated. This complication is because of the rocks are highly interlayered. Thermal gradients can be constructed smoothly in contact metamorphic terrains. However, the high grade terrains, like the SWHC suffered mostly regional metamorphism, collisional deformations, and interlayered rocks, give rather complicated thermal gradients which should be taken into consideration of thermal structure in these regions.
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`
Figure 36. Distribution of metamorphic temperatures in the studied area which is the same as the study area by Sajeev and Osanai (2005). Red lines indicate the current study. Black colored contours indicate the contours proposed by Sajeev and Osanai (2005). Green contouring is according to the Faulharber and Raith (1991) study for pressure
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